Entanglement entropy of singular surfaces under relevant deformations in holography
Abstract
In the vacuum state of a CFT, the entanglement entropy of singular surfaces contains a logarithmic universal term which is only due to the singularity of the entangling surface. We consider the relevant perturbation of a three dimensional CFT for singular entangling surface. We observe that in addition to the universal term due to the entangling surface, there is a new logarithmic term which corresponds to a relevant perturbation of the conformal field theory with a coefficient depending on the scaling dimension of the relevant operator. We also find a new power law divergence in the holographic entanglement entropy. In addition, we study the effect of a relevant perturbation in the Gauss-Bonnet gravity for a singular entangling surface. Again a logarithmic term shows up. This new term is proportional to both the dimension of the relevant operator and the Gauss-Bonnet coupling. We also introduce the renormalized entanglement entropy for a kink region which in the UV limit reduces to a universal positive finite term.
Cite
@article{arxiv.1709.08169,
title = {Entanglement entropy of singular surfaces under relevant deformations in holography},
author = {Mostafa Ghasemi and Shahrokh Parvizi},
journal= {arXiv preprint arXiv:1709.08169},
year = {2018}
}
Comments
21 pages. v2: 30 pages, title changed, one section regarding the renormalization added, minor corrections in text and equations